marriage wage premium with contract type heterogeneity
TRANSCRIPT
Marriage Wage Premium with Contract TypeHeterogeneity
Roberto Bonilla�, Newcastle University, UK
Miguel Á. Maloy, Universidad de Salamanca, Spain.Fernando Pinto, Universidad Rey Juan Carlos, Spain.
November 9, 2021
Abstract
We present a model of interlinked labour and marriage markets,both characterised by sequential search, where men are seen as bread-winners in the family. Two types of jobs exist �temporary and per-manent. Men�s reservation strategy in their labour market searchresults in two reservation wages - one for each type of job. Women�sreservation strategy in their marriage market search results in two dis-tinct reservation wages: for men on temporary jobs and for men onpermanent jobs, where the former is higher. This re�ects a trade-o¤between husband�s wage and type of contract. This generates equilib-ria with a positive marriage wage premium for all workers, but higherfor temporary workers. We successfully test our results using Span-ish data. Linked to this, we also �nd that permanent employmentis linked to higher wages among never married workers, but to lowerwages among married employees. We argue that the traditional ar-guments of specialisation and selection for a marriage wage premiumpredict the opposite results.Keywords: frictional markets, marriage premium, temporary and
permanent jobs. JEL Codes: D83, J12, J16, J31.
�Corresponding author: Newcastle University, Business School, 5 Barrack Road, NE14SE, United Kingdom. Tel.: +44 191208 1670. Email: [email protected]
yMiguel Á. Malo acknowledges funding from project SA049G19 (�Junta de Castilla yLeón�). The funding source had no involvement in the preparation of this article.
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1 Introduction
On average, married men seem to earn more than single men. This wage gappersists after controlling for systematic in individual attributes. Accordingto Daniel (1995), estimates range from 10 to 30%. Cohen and Haberfeld(1991), Nakosteen and Zimmer (1997) are two in�uential examples of thewide empirical literature on this topic. Crucially, the empirical evidenceseems to suggest no marriage wage premium for women.
The traditional explanations for the male marriage wage premium arebased on the concepts of "specialisation" and "selection". The selection hy-pothesis (see Nakosteen and Zimmer (1997) for an example) posits that someunobservable characteristics of men are valued not only in the labour marketbut also in the marriage market. Based on these unobservables, productivemen may be perceived as more attractive partners, thus generating the pos-itive correlation between wages and married status.. However, the empiricalevidence on this is quite weak. Ginther and Zavodny (2001) �nd that onlyup to 10% of wage premium is a result of selection, whereas Chun and Lee(2001) go even further and argue that the selection e¤ect is minimal.
In turn, the household specialisation argument originates in the work ofBecker (1993). It proposes that marriage increases a man�s productivity,following the labour market specialisation that is possible due to the supportof a wife. Korenman and Neumark (1991) provide some empirical supportfor this hypothesis. They �nd that wages increase after marriage, marriedmen get better performance evaluations and are promoted more frequently.
A growing body of empirical evidence shows that the di¤erence in wagesof married and unmarried men stems from selection into marriage directlybased on wages and wage growth - crucially, both observable. Grossbard-Shechtman and Neuman (2003) call this the "breadwinner" e¤ect. Going astep further, Ludwig and Brüderl (2018) propose that the traditional argu-ments of specialisation and selection should be discarded.
This, in fact, seems to re�ect existing evidence on the gender asymmetryin the interaction between labour market and marriage preferences and out-comes. For example, Blundell et al. (2016) show that female attachmentto the labour market weakens considerably after marriage. In turn, Gouldand Paserman (2003) suggest that increased male wage inequality leads to a
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decline in marriage rates for women. They also �nd that women are moreselective in the marriage market when female wages increase (a proxy for thevalue of being single relative to married) and that they are less selective whenmale wages increase (proxy for the value of being married relative to single).In all these, the analogue is not true for men. They conclude that their�ndings support a search model of the female marital market. Similarly Op-penheimer and Lew (1995) �nd that increased economic independence leadsto a delay in marriage for women, but not to a substantial decrease in theproportion of women who will marry. Oppenheimer (1988) calls this the �ex-tended spouse search�theory. Once again, they argue that the analogue isnot true for men. In all these studies, men�s economic potential is positivelyrelated to likelihood of marriage.
Bonilla and Kiraly (2013) introduced a theoretical framework of interre-lated frictional labour and marriage markets that captures the above asym-metries. They are the �rst to obtain a marriage premium as a result of searchfrictions, without relying on the traditional explanations: the result does notdepend in any way on any notion of specialisation or male heterogeneity (ob-served or unobserved). Instead, the causality is in the direction suggested byLudwig and Brüderl (2018). In Bonilla and Kiraly (2013), women choosea reservation match in their (marital) search e¤orts, and this translates intoa reservation wage such that they will not marry any employed man whoearns less than that. Aware of this, men�s job search is characterised by anoptimally chosen reservation wage which may be lower - that is, while theyof course hope for a high wage that would be acceptable to women, they willstill accept wages that imply women will reject them for marriage, providedthese wages are not too low. The gap between the male (labour market)reservation wage and the female (marriage market) reservation wage is whatgenerates the marriage wage premium.
The framework has proved useful to study related issues. For example,Bonilla et al (2019) introduce male heterogeneity as regards to the marriagemarket (some men are more attractive) and shows that the framework canexplain the existence of Beauty Premium - including its links to marriagepremium. The theoretical results are successfully tested using British data.Similarly, Bonilla et al (2021) introduce male heterogeneity as regards to thelabour market (some men are more productive than others), and it generatesa prediction of the ranking of the marriage premia across men of di¤ering
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productivities. This is tested successfully using Chinese data. In turn,Bonilla et. al (2017) introduces female heterogeneity as regards to the mar-riage market (some women are more attractive than others) and show thatthis can lead to class formation as in Burdett and Coles (1997), but based onthe exogenous distribution of productivities and the endogenous distributionof wages.
In this paper we extend benchmark framework in Bonilla and Kiraly(2013) by introducing male heterogeneity not in the male or the female sideof the market, but in the labour demand side: two types of jobs are available,some are temporary and some are permanent. This results in a clear testableprediction: The marriage wage premium that characterises men on perma-nent jobs is in general lower than that which characterises men on temporaryjobs, when a marriage premium exists at all. The reason is clearly linked tothe forces that generate the marriage wage premium in the �rst place: givena wage earned by the prospective husband, the future is nicer if his job ispermanent. As a result, women set lower marital reservation wages for menon permanent contracts, and this translates into lower marriage wage premiafor these men.
We test the model using Spanish data. Spain seems to be a very goodscenario to test our model for at least two reasons: First, the dualisation ofits labour market between temporary and permanent workers. In Spain, theshare of temporary contracts relative to all wage and salary workers reacheda peak of 33% at the beginning of the 1990s (Dolado et al., 2002), and hasremained above 20% including at the worst moments of the great recession,even though temporary workers where severely a¤ected by employment losses(International Labor Organization, 2014). Second, there is evidence that thelink between labour and marriage market dynamics di¤ers across genders ina way closely linked to the heart of the model: De la Rica and Iza (2005)�nd that there is a delay in the transition to marriage for men on unstablecontracts (or indeed not working) relative to men on open-ended contracts,but this di¤erence does not exist for women.
Our empirical results are in line with the predictions of the model: themarriage wage premium is higher for temporary workers. Deconstructing thisresult, we �nd that among never married workers, a permanent employmentis linked to higher wages. In stark contrast, it is linked to lower wages
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among married employees.. We see this as evidence that, ceteris paribus,women �select� higher earning men for marriage, and marry workers with�bad�features in the labour market -as a temporary contract- when this canbe compensated with higher earnings. We also present some robustnesschecks, broadly con�rming our results.
Crucially these results are opposite to what would be expected if special-isation or selection based on unobserved heterogeneity were the main forcesbehind the marriage wage premium. One would expect more labour marketspecialisation on men on permanent contracts. Following this, the marriagewage premium among men on permanent jobs should be higher. Regardingthe selection on unobservables argument, one would expect married men onpermanent job to exhibit more valuable labour market characteristics, andthis to be re�ected in a higher wage premium. Thus, this explanation wouldpredict a higher marriage wage premium among men on permanent jobs. Ifone considers that this is re�ected in the nature of the contract itself (openended vs temporary) instead of wages, then the selection on unosbervablesapproach does not result in a prediction related to the result in this paper.This view is, nevertheless, not supported by the fact that, overall, we observesingle men on permanent contracts earning higher wages than on temporarycontracts, but this is not true for married men.
Section 2 introduces the model in detail and derives steady state valuesfor the ensuing analysis, while Section 3 analyses optimal search by womenand men respectively. Section 4 addresses the equilibria and �nishes with adiscussion of the testable predictions, relative to the marriage wage premia.The empirical test is addressed in Section 5, while Section 6 concludes.
2 The model
Men enter the economy single an unemployed. They search sequentially forjobs, of which there are two types (type denoted by i): Permanent (i = p) orTemporary (i = t). We assume that unemployed men contact jobs of typei with exogenous arrival rate �i:The distribution of wages is common acrossjob types, and is denoted F (w); with minimum and maximum and wagesgiven by w and w and respectively. Simultaneously, single men meet womenat rate �w� this rate is the outcome of a quadratic matching function thatcharacterises search in the marriage market. Men take as given that women
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are picky, and only accept marriage to men employed in jobs of type i if theyearn wages not lower than Ti. If employed at wage w and single, men enjoy�ow payo¤ w. If married, men enjoy �ow payo¤ y > 0 in addition to thewage. Jobs of type i are destroyed at rate �i; with �t > 0 and �p = 0. Thereis a continuous �ow � of single unemployed men into the economy. Divorceis prohibited. In this environment characterised by sequential search, men�soptimal policy is to decide two reservation wages Ri such that they do notaccept employment in a job of type i if it pays less than Ri.
Women enter the economy single. While single, women enjoy �ow utilityx. Only when single, they meet employed men of type i at rate � i� these areendogenous and are the result of a quadratic matching function. A womanmarried to a man earning wage w enjoys �ow payo¤ w� we assume �owvalue x is given up upon marriage. In this environment, women�s optimalstrategy is characterised by two marital reservation wages Ti, such that theydo not marry a man employed in a job of type i if he earns less than Ti. Weassume that when a woman gets married, she is replaced by an identicalwoman. Hence the number of women, n can be treated as exogenous: Toavoid confusion with the male reservation wages in the labour market, werefer to these female reservation wage as cut-o¤ wages from now on.As in Bonilla an Kiraly (2013) and Bonilla et al. (2018) we will focus on
equilibria in which women do nor marry unemployed men. As is shown there,this equilibria are trivial and uninteresting because the marriage market doesnot a¤ect men�s labour market decisions.
2.1 Arrival rates, stocks, and wage distributions insteady state
Arrival rates. We address �rst the relevant arrival rates as a function ofthe steady state measures. In steady state, let u denote the measure ofsingle, unemployed men and Ni denote the measure of single-marriageablemen in type i contracts - in the sense that they earn a wage not lower thanTi. Further, let eNi denote the respective measures employed, unmarriageablemen. With with the measure of single women given by n, the number ofmeetings between a man and a woman is given by m = �(u + Nt + Np +eNt + eNp) where � is an e¢ ciency parameter. It follows that the rate atwhich a single man encounters a single woman is �w = �n: Similarly, the
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rate at which a woman meets a single marriageable man of type i is given bymn
Ni(u+Nt+Np+ eNt+ eNp) = �Ni:
Steady state stocks. We now turn our attention to the determination ofthe relevant measures of men in di¤erent states. With �p = 0; the stock ofsingle and unemployed men (u) is given by �ow in equal �ow out, or
u =� +Nt�t + eNt�t
�t[1� F (Rt)] + �p[1� F (Rp)]In the above, the �ow into u is composed of the exogenous �ow of men intothe economy plus the single men (marriageable and unmarriageable) in typet jobs who lose their job. Please note that married employed men also losejobs at the respective rates, but being married they do not fall back into thesingle and unemployed category. The �ow out of u includes men who acceptjobs of either type: they meet a job of type i that pays a wage not lowerthan Ri (recall that we consider equilibria where single men are not acceptedby women).
The stock of employed, unmarriageable men of type t, denoted eNt is givenby
u�t[F (Tt)� F (Rt)] = eNt�teNt =u�t[F (Tt)� F (Rt)]
�t
where the �ow in is given by the single unemployed men who accept jobs oftype t with wages below the cut-o¤ wage a woman would accept. The �owout is given by those who lose their job1.
Finally, the stocks of employed marriageable men in temporary jobs,which we denote Ni; solve (noting that we have assumed �p = 0)
u�i[1� F (Ti)] = Ni(�i + �n)
Ni =u�i[1� F (Ti)](�i + �n)
:
1The stock of unmarriageable men in jobs of type P never reaches a steady state sincethere is no �ow out. This is of no consequence for the analysis below. It could in anycase be addressed by introducing a rate at which men leave the economy.
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Here, the �ow in is given by single unemployed men who accept jobs of typei with a marriageable wage, while the �ow out includes men in this groupwho either lose their job or get married.
As shown in Appendix 1, substituting out eNi and Ni in u above leads to:u =
�(�t + �n)
�a�a = �t[1� F (Tt)]�n+ �p[1� F (Rp)][�t + �n]
and thus Nt and Np are given by
Nt =��t[1� F (Tt)]
�a
Np =�(�t + �n)
�a
�p[1� F (Tp)]�n
It is straightforward to show that �Np�Tt
> 0;and the intuition is quite interest-ing: ceteris paribus, as Tt increases, less men accept marriageable t jobs andeventually get married - these men would never fall back into the unemployedand single category (u). In addition, more men accept jobs with unmar-riageable wages, these men eventually fall back into single and unemployedcategory. Thus, the stock of single and unemployed men increases. Thisin turn means more men �ow into marriageable permanent jobs, resulting inan increase in Np:
Further, �Nt�Tt
< 0 as expected, since temporary jobs with marriageablewages are, ceteris paribus, more di¢ cult to �nd.
Steady state wage distributions. Following from the above, we nowcompute the distribution of wages among marriageable men of type i; thosewith wages higher than or equal to women�s respective cut-o¤ wage. Weuse Gi(w) to denote these distributions. The �ow of men into employmentat wages which are marriageable but less than w in type i jobs is given byu�i[F (w)�F (Ti)]; while the �ow out is given by NiGi(w)(�n+�i): Equatingthese and substituting out Ni yields
Gi(w) =[F (w)� F (Ti)][1� F (Ti)]
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3 Optimal search
Here we address the optimal search strategies. In this sequential job searchframework in which two types of jobs can be encountered, men optimallychose two reservation wages: one for each type of job. Since women arehomogenous from men�s point of view (marriage to any woman yields �owpayo¤ y), men always want to get married and there is no male marriagemarket reservation wage. In turn, women face a sequential search problemin which two types of unemployed men can be found (working in p or t jobs)and thus optimally choose two cut-o¤wages, one for men employed on t jobsand one for men on p jobs. We also address the conditions for women toreject unemployed men. We start by analysing women�s problem.
3.1 Women
We �rst derive the conditions under which women will reject marriage toan unemployed worker. For this, will be useful to obtain the reservationwage of a married unemployed workers. Using Ri to denote these two wages;Appendix 2 shows that the value attributed to married, unemployed men isgiven by UM =
Rp+y
r=
Rt+y
r; and that
Rt = Rp =�t
r + �t
wZR
[w �R] dF (w) + �pr
wZR
[w �R] dF (w) � R
Since marriage market is irrelevant to married men, their reservation wageis that of a stand alone search labour market. Indeed, this reservation wagesare not a¤ected by y, since marriage will never be lost. There are two reasonswhy this "baseline" reservation wage is the same for both types of jobs: First,search is not directed, so both di¤erent types of jobs are found while searchingin the same pool. Second, because the reservation wages equate the value ofworking at that wage and the value of unemployment, the job destructionrate -the only di¤erence across these two job types- does not make a Rt di¤erfrom Rp:Please note, the decision problem that we analyse relates to Ri and Ti:
Hence it is worth highlighting that R; although a fairly complicated object,is a function of parameter values only. Further, since x is not one of the
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parameters a¤ecting R, the latter can be considered as exogenous for thepurposes of the analysis below.
We denote WMU the value of marriage to an unemployed worker. Since
any wage the husband earns in the future is a public good within marriage,the value of marriage to an unemployed is determined by his job acceptancestrategy. Having solved for Ri; and using W
Mi (w) to denote the value of
marriage to a worker earning w in a type i contract, it follows that WMU
solves:
rWMU = �t
wZR
�WMt (w)�WM
U
�dF (w) + �p
wZR
�WMp (w)�WM
U
�dF (w)
where WMt (w) =
w+�tWMU
r+�tand WM
p (w) =wr. In the above, if the husband
�nds a job (permanent or temporary) at an acceptable wage, then he becomesemployed and the lifetime discounted value enjoyed by the woman changesaccordingly.
Finally, we deal with the lifetime discounted value of a women who aresingle, W S. At this point, we consider the possibility of marriage to un-employed workers, in order to determine the region in which women willoptimally reject it. They meet marriageable men in a type i job at rate Ni;which leaves them enjoying WM
i (w): They meet unemployed men at rate u;and if the accept them for marriage they enjoy WM
U . Hence, WS is given by
rW S = Nt
wZTt
�WMt (w)�W S
�dGt(w) +Np
wZTp
�WMp (w)�W S
�dGp(w) +
+u�WMU �W S
�dGt(w) + x
where Ni and Gi(w) are as above, = 1 if WMU � W S and = 0 otherwise.
Recalling that here WMi (Ti) =
Ti+�iWMU
r+�i; the reservation wages Ti are thus
de�ned byWMi (Ti) =W
S (1)
As a result, u�WMU �W S
�dGt(w) = 0 for W S � WM
U2. From here, we
have that �WS
�x> 0; and thus �Ti
�x> 0; for W S � WM
U :
2Because = 0 if WS > WMU and = 1 but WM
U �WS = 0 if WMU =WS
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Since we are interested in the relationship between W S and WMU , and
noting that �WM
�x= 0; it is useful to de�ne x such that W S(x = x) = WM
U :From WM
i (Ti) = WS; we have that WM
i (Ti) = WS = WM
U at x = x; and itfollows immediately that W S(x) = Ti
rfor i = t; p: A consequences of this is
that Tt(x) = Tp(x) � Tx: Since WMt (w) �WM
U = w�Tir+�t
when x = x; we canuse all this in WM
U to obtain that, x = x; Tx solves:
Tx =�t
r + �t
wZR
[w � Tt(x)] dF (w) +�pr
wZR
[w � Tp(x)] dF (w)
and thus Tx = R3. Hence, for any x = x we have W S = WMU and Tt; Tp =
R: In this case, women do not accept unemployed men for marriage. Equallyimportant, for any x < x we have W S < WM
U and Tt; Tp < R: In this case,women accept unemployed men for marriage.
This is an important result regarding the impact the marriage market hason men�s job search strategy. Intuitively, there is a female �ow value whensingle x such that:
i) If x < x; then women�s cut-o¤ wages are lower than the reservationwage men would use if they did not consider the marriage market (R). Itis straightforward to show that if this is the case, men�s optimal reservationwage is R for both types of jobs. The intuition is as follows: The onlyincentive men could have to increase their reservation wage above R is relatedto marital purposes, but if R is enough for them to be marriageable, then Ris optimal even when men take into account the constraints in the marriagemarket. Please note the signi�cance of this: the marriage market does nota¤ect men�s labour market decisions.ii) If x = x; then men �nd that R is not enough to be marriageable, and
thus have an incentive to increase their reservation wage. We show belowthat indeed men�s reservation wages are higher than R in this scenario.Following i) and ii) above, we work from now on on the scenario x > x:
Turning our attention to the relationship between the female cut-o¤wages(Ti), Proposition 1 below shows that women apply a higher Ti to men on tem-porary jobs is higher than to men on permanent jobs. The intuition behind
3It can be shown that Ti(x) ? R both lead to a contradiction.
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this is that, given the wage earned by the prospective husband, marriage tohim is nicer if his job is permanent rater than temporary.
Proposition 1 Tt > Tp:
Proof. We know Tt+�tWMU
r+�t= Tp
r(=W S) in equilibrium, or
Ttr � [r + �t]Tp = �r�tWMU
First, note that r�tWMU is independent of x, and when x = x we have WM
U =W S = R
rand Tt = Tp = R: In this case, the above equality is satis�ed.
For x > x; �r�tWMU does not change, but Ttr � Tp[r + �t] changes since Ti
both increase. Denote the respective increments �Tt and �Tp . For theequality to hold, �Tt and �Tp must be such that r�Tt � [r + �t]�Tp = 0 orr�Tt = [r + �t]�Tp. Since r < r + �t; it must be that �Tt > �Tp; whichmeans that Tt > Tp for any x > x:At this point is important to highlight that, as shown in the proof of
Proposition 1, there is indeed functional link between Tp and Tt since it willbe useful in the analysis below.
3.2 Men
Here we derive the two reservation wages chosen by unemployed men: onefor each type of job. We will show that the reservation strategy is di¤ersqualitatively for di¤erent ranges of the female cut-o¤ wages, which men takeas given.
The reservation wage men would use in a stand alone labour market (equalto that of married unemployed men) plays an important role in the analysisof single unemployed men search strategies. We reproduce R(= Rt = Rp)here from Section 2:
R =�t
r + �t
wZR
[1� F (w)] dw + �pr
wZR
[1� F (w)] dw
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3.3 Single unemployed men
Below we address separately three possible outcome con�gurations in termsmen�s job market reservation wages relative to women�s marriage market cut-o¤ wages. In the next section we pin down the values of x required for eachof these con�gurations to obtain in equilibrium.
Con�guration 1: R < Ri < Ti for i = t; pTo address this scenario, recall �rst that when R < Ti we have that
unemployed men are rejected by women. Then the value of an unemployedand single man, which we denote U , solves
rU = �p
wZRp
[V Sp (w)� U ]dF (w) + �twZRt
[V St (w)� U ]dF (w): (2)
Here, a man who is unemployed and single meets jobs of type i at rate �iand accepts them if they o¤er wages not lower than the chosen Ri: Thevalue of accepting any given wage w, V Si (w); depends on whether it is a"marriageable" wage or not. Because Ri < Ti; men will accept wages thatbelong to the range [Ri; Ti) and preclude marriage. Thus we have:
V Si (w) =
(w+�iUr+�i
if w < Tiwr+�i
+ �iU(r+�i+�n)
+�n[y+�i R+yr ]
(r+�i+�n)(r+�i)if w � Ti
):
4The discontinuity of V Si (w) at w = Ti is a result of the marriageability atwages equal to Ti or higher.
Following this, men who accept jobs at the reservation wage are not mar-riageable so V Si (Ri) =
Ri+�iUr+�i
: Further, from the de�nition of reservationwage Ri; we know U = V Si (Ri) and hence V
Si (Ri) =
Rir= U for both i = t; p:
Note that his men apply the same reservation wage to both types of jobs.The key to understanding this result is that the only di¤erence across jobs isthe job destruction rate, and because the reservation wages equate the valueof employment and unemployment, the di¤erence in job destruction rate doesnot draw a gap between the two Ri:
4For w � Ti we use rV Si (w) = w + �i[U � V Si (w)] + �n[VMi (w) � V Si (w)] and thevalue of being married and earning w as VMi (w) = w+y+�iU
M
r+�i; with UM = R+y
r as derivedbefore.
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Using all this in U , the common reservation wage can be derived (asshown in Appendix 3),
R =Xi=t;p
24 �ir + �i
wZR
[1� F (w)]dw + �i�n[1� F (Ti)][r + �i + �n][r + �i]
�y + �i
�R + y
r� Rr
��35(3)
where, recall, UM = R+yr: As was the case for the "baseline" reservation wage
R, the reservation wage of unemployed single men must compensate for theloss in the value of continued search. But now, because Ri < Ti; acceptingthe reservation wage implies giving up any chance of marriage in the future,which would have been kept alive had the wage not been accepted in favourof continued search. As a result, the reservation wage must also compensatefor this loss of "marriageability": Finding a job at a marriageable wage(�i[1� F (Ti)]) and then a woman who would have accepted marriage (�n);all properly discounted, and accounting foe the the risk of unemployment inthe future.
From the reservation wage equation above, it can be shown that �R�Ti
<0 if R < Ti < w: As either Ti increases, the probability of encounteringmarriageable wage decreases, and with it the value of marriageability. Thisis re�ected in a decrease of the reservation wage. This intuition should becomplemented by noting that if Ti are high enough, then the optimal malereservation wage is lower than Ti re�ecting the high labour market cost ofincreasing reservation wages above the "baseline" reservation wage R: Itfollows that there is a Ti low enough that R < Ti stops to hold.
Further, it is straightforward to show that �R�Ti
= 0 if Ti � w: Whenwomen are so picky that they require wages higher than the highest wagein the market from men on temporary and permanent jobs, then we obtainR = R: However, when women are not that picky and Tt � w but Tp < w;then marriageable wages exist if on a permanent contract. Then we havethat R > R; re�ecting the incentives related to the marriage market thatcome from this.
Proposition 2 below states that this con�guration describes men�s optimaljob search strategy if both female cut-o¤ wages are high enough.. Beforestating Proposition 2, we de�ne a threshold value of female cut-o¤ wages
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for permanent workers such that men�s reservation wage for permanent jobsis equal to this cut-o¤ wage. We denote this bTP ; and our de�nition yieldsR = bTp in equation (3). Given that Tt > Tp; it is clear that as Ti decrease,R will hit Tp �rst: R = Tp occurs when R < Tt.
Proposition 2 If Tp�[bTp; w]; then men�s optimal search strategy is describedby reservation wages that solve (3); and Ri < Ti in the whole range.
Proof. Follows from the derivation of (3) and noting that �R�TP
< 0: Then for
Tp < bTp we have R > Tp and Con�guration 1 is broken. When Tt � w andTp < w then F (Tt) = 0 in (3). When Tp � w; then F (Tt) = F (Tp) = 0 in(3).The threshold value bTp corresponds to a particular value of the female
reservation wage for men on temporary jobs, which we call Tt(bTp) (fromSection 3.1 we know that Ttr�[r+�t]Tp = r�tWM
U ): The two panels in Figure1 depict the above male reservation wage against TP and TT respectively.Following from Proposition 2, there is a di¤erent con�guration of Ri relativeto Ti for Tp < bTp: This is addressed in the sub-section below.Figure 1 around here
Con�guration 2: Rp = Tp; Rt < TtAppendix 4 shows that if Rt < Tt; then it is never optimal to set a
reservation wage for p jobs higher than the cut-o¤wage women apply to menon p jobs: setting the former equal to the latter already implies the manis marriageable after accepting employment, so increasing Rp further willjust delay marriage because it delays employment, itself a pre-condition formarriage in equilibrium. This is in addition to the labour market loss relatedto increasing the reservation wage above R. Then, for Tp = bTp � ", men�sreservation strategy is characterised by Rp = Tp as it regards to permanentjobs. In relation to temporary jobs, the reservation wage is still determinedby the standard de�nition U = V St (Rt):Hence Rt = rU where
rU =�pr
wZTp
[1� F (w)]dw + �p�n[1� F (Tp)][r + �p + �n][r + �p]
���pRpr
+ y + �pUM
�(4)
�tr + �t
wZRt
[1� F (w)dw + �t�n[1� F (Tt)][r + �t + �n][r + �t]
���tRtr
+ y + �tUM
�
15
Clearly �Rt�Tp
< 05: The intuition behind this is analogue to the one addressedin Con�guration 1, while the intuition for the strategy forRp has been alreadyhinted at: If Tp is not high enough (i.e. lower than bTp), then the labourmarket cost of "matching" it by setting Rp = Tp is lower than the marriagemarket related bene�ts: ensure marriageability after employment.
Proposition 3 below states that this Con�guration describes men�s opti-mal job search strategy if female cut-o¤ wages are not too high and not toolow. We de�ne bTt such that R(bTt; Tp) = bTt in (4), a threshold value of Ttthat plays a role analogue to bTp for permanent jobs. As Tp; Tt both decrease,it is possible for Tp to hit R before Tt hits bTt or the other way around. Toaddress this, recall that Tt+�tW
MU
r+�t= Tp
r. It follows that Tp(bTt) = r(bTt+�tWM
U )r+�t
.
If Tp(bTt) > R; then it is possible for both Tp and Tt to be in the range [R ; bTp]:Whether this is the case or not is a matter of parameter values only. Herewe work under the assumption that this is the case.
Proposition 3 For Tp�[Tp(bTt); bTp];men�s optimal search strategy is describedby Rp = Tp and Rt that solves (4); with Rt < Tt in the whole range.
Proof. Follows from the derivation of (4), noting that �R�Tt
< 0 and the
assumption that Tp(bTt) > R: Then for TP = Tp(bTt) we have that Tt = bTt. Amarginal decrease in Tt; Tp results in Tp > R and Tt < bTt , R(Tt; Tp) > Tt:The latter inequality violates Con�guration 2.
From Proposition 2 and inspection of Figure 1, it is clear that con�gura-tion is broken for TP < Tp(bTT );which leads to the third possible con�gurationin the subsection below.
Con�guration 3: Ri = Ti for i = t; p:In this con�guration, women�s cut-o¤ wage for men in both types of
contracts is quite low, and this gives incentives for all men to they are mar-riageable after employment. The results here follow immediately from theanalysis of the two previous con�gurations. Proposition 3 formalises this:
Proposition 4 For Tp�[R; Tp(bTT )] we have that men�s optimal search strat-egy is described by Ri = Ti:
5This is also depicted in Figure 1, where the slope of Rt(Tt) on Tt changes at Tt( bTp)� because of the di¤erent Rp to either side of bTp:
16
Proof. It follows from Proposition 1 and 2 that using Rp < Tp and/orRt < Tt leads to a contradiction. It is easy to show that Ri = Ti is alwaysbetter than Ri > Ti:
Having analysed in detail men�s and women�s strategies, we know turnour attention to equilibrium con�gurations in the next section.
4 Equilibrium
Here we address the market equilibrium. Following the three possible con�g-urations addressed in the previous section, the three equilibria in De�nition1 below correspond to each of the three con�gurations studied: An equi-librium in which the relationship between Ri and Ti mirrors Con�guration1(2,3) is referred to as a Type 1(2,3).We �nish by commenting on the implications regarding male marriage
wage premium and transitions to marriage, and the di¤erences across thetwo types of equilibria. For this, we �rst de�ne the marriage wage premiumof men on contracts of type i �denoted MPi� as the di¤erence betweenthe average wage of the employed married men and the average wage of thesingle employed men �denoted wMi and wSi respectively. Then, MPi =wMi � wSi . It is easy to show that MPi R 0 if Ti R Ri and that thesize of this marriage wage premium increases with the di¤erence Ti � Ri:6This of course follows from the simple observation that the wages amongmarried employed men are distributed F (w)=[1 � F (Ti)], while the stock ofsingle employed men includes those with unmarriageable wages, which aredistributed F (w)=[F (Ti)� F (Ri)]:
De�nition 1 i) A Type 1 equilibrium is a triplet R�; T �p ; T�t where R
� <T �p < T
�t , R
� solves (3), and T �i solve (1).ii) A Type 2 equilibrium is a quadruple R�p; R
�t ; T
�p ; T
�t where Rp = Tp; Rt <
Tt; R�t solves (4) and T
�i solve (1).
iii) A Type 3 equilibrium is a quadruple R�p; R�t ; T
�p ; T
�t where R�p =
T �p ; R�t = T
�t ; and T
�i solve (1).
6Please see Bonilla and Kiraly (2013) and Bonilla, Kiraly and Wildman (2018) for adetailed derivation.
17
Theorem 1 An equilibrium exists for Tp > R:i) A Type 1 obtains if x, women�s value as single, is high enough.ii) A Type 2 obtains for mid-range values of x.iii) A Type 3 equilibrium obtains for low values of x.
Proof. To start, note that women�s strategy determines Tp and Tt functionsthat are continuous on Ri and x;while �Ti
�x> 0 and �Ti
�Ri> 0:To address
Type 1 equilibria, note that R(Tt; Tp) as described by (3) is continuous onTp and Tt. Following Proposition 1, de�ne xp such that T �p (xp) = w;andbxp such that T �p (bxp) = R�(bxp)(= bTp): Because �R(Tt;Tp)
�x= 0; while �Ti
�x> 0;
this type of equilibrium obtains if x � bxp. Tuning our attention to Type2 equilibria, it is clear that R(Tt; Tp) as described by (4) is continuous onTp and Tt. Following Proposition 2, de�ne xP such that T
�P (exP ) = Tp(bTT ).
Because �R(Tt;Tp)
�x= 0; while �Ti
�x> 0; this type of equilibrium obtains if for
x 2 [exp; bxp): To address Type 3, it follows from all the above and Proposition3.Figure 2 below depicts equilibria of Type 1 and Type 2.
Figure 2 around here.
We now address the main predictions of our model, which relates to themarriage wage premia and ranking across job types, and will form the basisof our empirical implementation.Corollary 1, which relates to the ranking of marriage wage premia across
job types, and follows from our de�nition of marriage wage premium andTheorem 1 above:
Corollary 1 MPt > MPp if x�[exp; xwp ]; while MPt = MPp = 0 if x�[xp; exp]Proof. When x� [xp; xwp ] a Type 1 equilibrium obtains. In this equilibrium,MPt > MPp because Rp = Rt while Tp < Tt: When x�[exp; bxp] a Type2 equilibrium obtains. In this equilibrium, MPt > 0; MPp = 0 becauseRp = Tp and Rt < Tt:When x�[xP ; exP ] a Type 3 equilibrium obtains. Inthis equilibrium, MPi = 0 for i = p; t because Ri = Ti for i = p; t:
18
5 Empirical analysis
We now proceed to test the implications detailed in Corollary 1. As explainedbefore, we use data from Spain, due to the duality of the labour market, wheremarriage decisions and outcomes are likely to be interrelated with the labourmarket. To this end, we estimate di¤erent wage equations for male workershired under two di¤erent types of contracts: open-ended and temporary .As expected, average wages earned by men on permanent jobs are higher
than for those on temporary jobs for the whole sample and when only nevermarried workers are considered. Parallel to this, a permanent job is attachedto a positive estimated coe¢ cient. Crucially, the opposite is true when onlymarried employees are considered: the coe¢ cient attached to a permanentjob is now negative. This is re�ected in a higher marriage wage premiumfor men on temporary jobs. To further control for heterogeneity, we run tworobustness checks related to this, in which we split the sample by educationtype and then using both education and contract type. The empirical resultsbroadly con�rm our theoretical predictions.
5.1 Data and Summary Statistics
Our database consists of the Spanish data of the European CommunityHousehold Panel (EHCP) from 1994 to 2001. In this period, Spain had thehighest temporary employment in Europe as a share of total employment,around 30% (Dolado et al., 2002). The time period corresponds to a morerestrictive divorce law than the current one, with a markedly higher cost ofdivorce. In addition, cohabitation did exist during those years, but it wasnot as extended as it is now (Castro-Martin, 2013).For the period 1994-2001, the Spanish sample of the ECHP included
8,000 households/year. These individuals were interviewed every year, evenif the household split. The database includes rich and detailed informationon income and socioeconomic characteristics. We have information on ourkey variables, as gender, the type of contract, marital status, and income. Inaddition, we can consider the following control variables: economic sector,region, age, and if they have children above 12. Likewise, it also providesdata on education level which we use to test the models within educationtypes, to check for robustness of the results.We use the log of labour income from the previous month as dependent
variable. We do not use the hourly wage because the information on working
19
hours is limited for part time workers and we would restrict our sample size.Following the theoretical model, we only include men who were working theprevious month, who are either in their �rst marriage or have not yet married.Those cohabiting are considered not yet married.Table 1 shows the summary statistics. The percentage of men with a
temporary contract is 27.85%, which is consistent with previous evidence ofthe Spanish labour market (Dolado et al., 2002; Bentolila et al., 2012; ILO,2014).Log monthly wages are higher for those with an open-ended contract. At
the same time, the proportion of married men is seven times higher for thosewith an open-ended contract (73.8% versus 10.1%). This correlation is alsoa¤ected by other variables such as age or education level. The majority havean education level equal to or lower than school. On the other hand, we have28.2% percent of individuals with a university degree or higher , while thosewith high school only correspond to 20.8% of the observations. Those withan open-ended contract have less children above 12.
Table 1 around here
Finally, the sample average age is 36. As for the distribution by eco-nomic sector, 4.7% of the sample work in the agricultural or primary sectorcompared to 44.6% in the industrial sector, and 50.7% at the service sector.
5.2 Wage regressions
We run regressions to estimate to explore the correlation between maritalstatus and wages, and regressions to explore the e¤ect of the type of contracton the whole sample, on married men, and on never married men.For the former we estimate the following �xed-e¤ects linear regression:
ln(wit) = �1Marriageit + 01Xit + ai + �it
Here, ln(wit) is the natural log of monthly wages, Marriageit is a dummyvariable for marital status, Xit denotes a matrix of control variables, ai is theindividual speci�c time-invariant heterogeneity -i.e. the �xed-e¤ects-, and�it is the standard idiosyncratic error term. The coe¢ cient of interest is �,which measures the correlation between marriage on the (log of) monthlywages, or, in other words, the marriage wage premium (MWP). The control
20
variables included in Xit are age, economic activity sector, if they have chil-dren above 12 cohabiting in the household, and region. Note that we cannotinclude control variables constant across time, as the educational level, be-cause they are subsumed in the �xed-e¤ects term. We use this information inthe robustness checks where we estimate di¤erent equations by educationallevel.Following Corollary 1, we are interested in comparing the MWP across
contract types. Therefore, we will run the above regression also by contracttype - either temporary or open-ended. Following the theoretical model,we use the type of contract at the time of marriage. An alternative optionwould be introducing a dummy variable for the contract type. With thatapproach, we should also introduce an interaction of the contract type andmarriage variables, to account for this interaction. That procedure assumesthat the e¤ect of the other variables on wages is the same irrespective ofthe type of contract, which is not supported by previous literature -see, forexample, Davia and Hernanz (2004). For practical reasons, that approachwould be a lesser evil if the sample sizes were not large enough to obtainreliable estimations. Fortunately, we have a large sample size in all our mainregressions, as well as those by educational level and contract type.To investigate the link between type of contract and wages (for the full
sample and the two sub-samples indicated above) we estimate the followingregression, also using �xed e¤ects:
ln(wit) = �2contract+ 02Zit + ai + �it
Where ln(wit) is the natural logarithm of monthly wages, contract denotesthe type of contract of the individual in the form of a dichotomous variablethat will take the value 1 if the contract is permanent and 0 if it is temporary.On the other hand, the model includes a set of control variables under theexpressionXit (age, economic activity sector, children cohabiting, and region)and the �xed e¤ects operator, ai. Finally, as always, the model error term isincluded �it. In our speci�c case, � will be the coe¢ cient to be interpreted,which will allow us to know the e¤ect of the type of contract on wages, bothfor the general sample and for the individual samples of single and marriedpeople.
21
5.3 Analysis and results
As a �rst step, Table 2a shows that men on an open-ended contract earn al-most 12%more than those on a temporary contract (�xed e¤ects estimation).We also include an OLS regression to show that controlling by unobservedheterogeneity decreases to some extent this wage gap. This is consistent withprevious literature. For example, Jimeno and Toharia (1993) found a wagegap of 10% for workers with open-ended contracts respect to those with atemporary contract in Spain -including both genders in their estimations.
Table 2a around here
We do a similar exercise for two sub-samples: married men and nevermarried men. As shown in the tables in Appendix 5, we �nd that fornever married men, the coe¢ cient attached to employment in a permanentcontract is positive, matching the result for the whole sample. Turning tomarried men, the coe¢ cient attached to employment in a permanent contractis actually negative. We see this as directly linked to the fact that wagesand type of contract of men are traded o¤ from the potential wife�s point ofview, and as the building blocks of our results regarding the marriage wagepremium, which we discuss below.
Table 2b below shows the results for the marriage wage premium for thewhole sample and by contract type. The �rst column, �Overall Model�,includes all individuals and shows how the wage di¤erence between marriedand single men is 5 percent. We also �nd a marriage is statistically signi�cantfor men on open ended and on temporary contracts. Married men with anopen-ended contract earn almost 7 percent more than non-married men withthe same type of contract. Matching our theoretical predictions, the e¤ectof marriage for men on temporary contracts is higher: they earn almost 10percent more than their non-married counterparts.
Table 2b around here
5.4 Robustness check
We know that male temporary workers with university education will havebetter job options, including the availability of open-ended contracts (Malo
22
and Cueto, 2013), and this is likely to a¤ect their wages and, potentially, thesize of their marriage wage premia. To account for this heterogeneity, we runtwo robustness checks involving data on education.The �rst one is a set of estimations by educational level, shown on Table
3. The results on men with �degree or more� mirror the results on theoverall sample as it relates to our theoretical model: the coe¢ cient attachedto the �marriage� dummy is higher for men on temporary jobs. For menwith lower school level or less, the respective coe¢ cients are not statisticallysigni�cant. This is also consistent with our theoretical predictions (whichwould not be the case had the marriage wage premium of temporary workersbeen higher) . For men with high school education, we obtain a positive andsigni�cant marriage wage premium for those on permanent contracts, yetmarital status seems not to be signi�cant for men on temporary contracts. Apossible explanation for this might be the relatively lower wage di¤erentialsamongst the di¤erent groups and/or a low absolute level of wages. Thiswould, e¤ectively, group men with high school on temporary contracts withlowly educated men. This could re�ect the result in Bonilla et al. (2017),whereby men that can only earn low wages form part of a �last class� inwhich women marry men regardless of their wage or employment status, dueprecisely to their low wages.
Table 3 around here
We run another robustness check aggregating males in two groups, fol-lowing the results obtained in Table 3. Group A is composed of those maleworkers with a positive marriage wage premium -corresponding to the �rstthree columns in Table 3. That is, group A would be composed of indi-viduals with a university and higher education level with permanent andtemporary contracts, plus those individuals with a secondary education leveland permanent contracts. Group B comprises the rest of the observations,that is, those men whose educational level is secondary education and whohave a temporary contract, plus all males with the lowest educational level,regardless their type of contract.Table 4 shows the e¤ect of marital status on log wages for both groups
by type of contract. The results are coherent with the model. For Group Awe �nd again a positive marriage wage premium for both types of contracts,but larger for males with temporary contracts (14 percentage points versus9.5 percentage points). For the Group B, we do not obtain signi�cant results
23
for any type of contract. Therefore, we consider that the results obtained inTable 3 are robust.
Table 4 around here
6 Conclusion
In this article, we expand the theoretical and empirical literature on the mar-riage wage premium. First, we present a theoretical model (an adaptationof Bonilla and Kiraly, 2013), where marriage and labour markets are inter-connected, and there is heterogeneity in the labour demand side due to thepresence of two types of jobs: temporary and permanent. The model predictsthat the marriage wage premium will be lower for men on permanent jobsthan on temporary jobs. Given a wage for the future husband, women wouldprefer someone with a permanent job, because of the more stable expectedearnings of these workers. Therefore, they set a lower marital reservationwage for males on permanent contracts. Previous empirical literature showsresults according to this prediction. For example, De la Rica and Iza (2015)�nd a delay in the marriage age for males with unstable contracts (it is worthnoting that this delay does not exist for women). Thus, the model has animplication not really intuitive in the absence of formal analysis: males withtemporary contracts will marry only when they enjoy higher enough wages.As a consequence, we should observe a higher marriage wage premium formale temporary workers.We test this prediction using data from Spain, a country very suitable
for this empirical analysis because of the high share of temporary contracts,ranging from 25 to 33 percent since the mid-eighties of the past century(Dolado et al., 2002). As predicted, we �nd that married men with perma-nent contracts earn 7 percent more than never married men with the sametype of contract, while married men with temporary contracts earn almost10 percent more than never married temporary workers. We also presentestimations by educational level. The results are in line with the model formen with a university degree, who are those for whom a larger wage di¤eren-tial is expected. For lower educational levels, especially for males with onlycompulsory education, expected wage di¤erential are probably so low thatthey are not important for women to consider in their marital decisions.
24
Importantly we argue that "specialisation" and selection on unobservablesas a source of marriage wage premium would both yield predictions oppositeto our theoretical and empirical results.Therefore, we add to the literature on marriage wage premium not only
remarking again the importance of the interaction of two frictional marketsunder constrained search (Bonilla and Kiraly, 2013; Bonilla et al., 2019), butalso showing that the features of the jobs -here, the divide between temporaryand permanent contracts- may be crucial to understand how sometimes themarriage wage premium is larger for workers with �bad�features. Absent avery high wage, these males -here, temporary workers- would not be married.To sum up, we show that heterogeneity in the demand side of the labour
market is also potentially important to understand the marriage wage pre-mium. This opens the door to further research enriching the analysis of themarriage wage premium considering di¤erences related to the di¤erent char-acteristics of jobs and even �rms, or even analysing the relative importanceof heterogeneity in the supply and demand sides of the labour market fromtheoretical and empirical perspectives.
Competing InterestsRoberto Bonilla declares there are no competing interests.Miguel Á. Malo declares there are no competing interests.Fernando Pinto declares there are no competing interests.
FundingMiguel Á. Malo acknowledges funding from project SA049G19 (�Junta deCastilla y León�). The funding source had no involvement in the preparationof this article.
25
7 Appendices 1-5
Appendix 1. Steady StatesDirect substitution and bringing the denominator on the right hand side
to multiply on the left hand side yields
u (�t[1� F (Rt)] + �p[1� Fp(Rp)]) = �+[u�t[1� F (Tt)](�t + �n)
]�t+[u�t[F (Tt)� F (Rt)]
�t]�t
Moving the last two elements on the right hand side to the left and simplifyingyields
u
�[�t[1� F (Tt)](�n)
(�t + �n)] + �p[1� Fp(Rp)]
�= �
Finally multiply across by (�t + �n) to obtain u�a = �(�t + �n):
Appendix 2. Reservation wage of married and unemployed work-ers (R):Using UM to denote the value of being unemployed and married and
V Mi (w) to denote the value of employment in jobs of type i while married,we have
rUM = y + �t
wZRt
�V Mt (w)� UM
�dF (w) + �p
wZRp
�V Mp (w)� UM
�dF (w)
with V Mi (w) =w+y+�iU
M
r+�i:The reservation wages solve V Mi (Rt) = V
Mi (Rp) =
UM which implies UM =Rp+y
r=
Rt+y
r: Noting that V Mi (w) � UM =
w�Rtr+�t
;
we use all this in UM above and simplify to obtain the standard formula fora reservation wage:
Rt = Rp =�t
r + �t
wZR
[w �R] dF (w) + �pr + �p
wZR
[w �R] dF (w)
where we are using �p = 0:
Appendix 3
26
For w < Ti; we have V Si (w)� U = w�rUr+�i
:
For w � Ti we know V Si (w)�U = wr+�i
+ �iU(r+�i+�n)
�U +�n �n[y+�iUM ](r+�i+�n)(r+�i)
:
Now add and substract �n�iU(r+�i+�n)(r+�i)
V Si (w)�U =w
r + �i+
�iU
(r + �i + �n)�U+ �n�iU
(r + �i + �n)(r + �i)+�n�y + �iU
M � �iU�
(r + �i + �n)(r + �i)
Since �iU(r+�i+�n)
� U + �n�iU(r+�i+�n)(r+�i)
= �rUr+�i
; this is now
V Si (w)� U =w � rUr + �i
+�n�y + �iU
M � �iU�
(r + �i + �n)(r + �i)
Hence, (2) can be written
rU =Xi=t;p
�i
TiZRi
w � rUr + �i
dF (w) +�i[1� F (Ti)]�n
(r + �i + �n)(r + �i)
�y + �p(U
M � U)�
For Ri < Ti, we have V Si (Ri) =Ri+�iUr+�i
: Together with the de�nition ofreservation wages, U = V Si (Ri); we know U = V
Si (Ri) =
Rir; and this in turn
implies Rt = Rp = R: Together with UM = R+yrthis in the above yields
equation (3).
Appendix 4. Rp = Tp is preferred to Rp > TpFor any RP � TP ; we have RT < TT we have
rU =�p
r + �p
wZRp
[1� F (w)]dw + �p�n[1� F (Rp)][r + �p + �n][r + �p]
�y + �p
�UM � Rp
r
��
�tr + �t
wZRt
[1� F (w)]dw + �t�n[1� F (Tt)][r + �t + �n][r + �t]
���tRtr
+ y + �t(UM � Rt
rg�
the di¤erence being that now changes in RP a¤ect the rate at which mar-riageable wages are accepted, which is not the case when RP < TP : It isthen easy to show that �U
�RP< 0:
27
Appendix 5. The link between wages and type of contract for married andnever married men.
Tables A5a and A5b here
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[24] Nakosteen, R.A., Zimmer, M.A. (1997) Men, money and marriage: Arehigh earners more rpone than low earners to marry? Scial science Quar-terly 78
[25] Oppenheimer, VK (1988). A theory of marriage timing. The AmericanJournal of Sociology 94: 563�91.
[26] Oppenheimer VK , Lew V (1995) American marriage formation in the1980s: how important was women�s economic independence? In: Op-penheim Mason K, Jensen AM (ed) Gender and Family Change in In-dustrialized Countries. Clarendon Press, Oxford, UK.
30
45𝑜𝑜
Figure 1: Male reservation wages.
Panel (a)
�𝑇𝑇𝑝𝑝 �𝑤𝑤�𝑇𝑇𝑡𝑡
𝑅𝑅
𝑇𝑇𝑝𝑝
�𝑇𝑇𝑝𝑝
𝑅𝑅𝑃𝑃(𝑇𝑇𝑃𝑃)
𝑅𝑅𝑡𝑡(𝑇𝑇𝑡𝑡)
�𝑤𝑤
𝑅𝑅
45𝑜𝑜 𝑇𝑇𝑡𝑡
�𝑇𝑇𝑡𝑡
Panel (b)
𝑇𝑇𝑡𝑡( �𝑇𝑇𝑝𝑝)𝑇𝑇𝑝𝑝( �𝑇𝑇𝑡𝑡)
Figure 2: Market Equilibrium for Various x.
�𝑇𝑇𝑝𝑝
𝑅𝑅
𝑇𝑇𝑝𝑝
�𝑇𝑇𝑝𝑝
𝑅𝑅𝑝𝑝(𝑇𝑇𝑝𝑝)
�𝑤𝑤45𝑜𝑜
𝑇𝑇(𝑥𝑥 ∈ [ �𝑥𝑥𝑝𝑝, �𝑥𝑥𝑝𝑝))
𝑇𝑇𝑝𝑝( �𝑇𝑇𝑇𝑇)
𝑇𝑇(𝑥𝑥 ∈ [ �𝑥𝑥𝑝𝑝, �𝑥𝑥𝑝𝑝])
Table 1. Summary statistics: Men. Observations (N * T).
Overall Open-ended Temporary
Variable Mean Std. Dev. Mean Std. Dev. Mean Std. Dev.
Temporary contract (1=yes) 0.2785 0.448 0.000 0.000 1.000 0.000
Log monthly wage 12.299 0.614 12.496 0.532 12.184 0.629
Married 0.303 0.459 0.738 0.439 0.101 0.302
Age 36.95 10.99 39.46 10.50 32.14 10.28
Children 0.563 0.495 0.344 0.475 0.665 0.471
Degree or more 0.282 0.449 0.324 0.468 0.192 0.394
Higher school 0.208 0.406 0.216 0.411 0.193 0.394
Lower school or less 0.509 0.499 0.459 0.498 0.615 0.486
North-West 0.127 0.333 0.121 0.326 0.131 0.337
North-East 0.142 0.349 0.164 0.371 0.131 0.337
Community of Madrid 0.099 0.298 0.126 0.332 0.086 0.280
Center 0.146 0.353 0.141 0.348 0.148 0.355
East 0.203 0.402 0.225 0.417 0.193 0.395
South 0.209 0.406 0.165 0.371 0.229 0.420
Canary Islands 0.071 0.258 0.055 0.228 0.079 0.270
Agriculture 0.047 0.211 0.027 0.163 0.088 0.0284
Industry 0.446 0.497 0.402 0.490 0.538 0.498
Services 0.507 0.499 0.569 0.495 0.373 0.484
NOTE: For the sample as a whole. 56.80% are men and 43.20% are women. A total of 21,330 men; 68.27% with a
temporary contract and 31.73% with a permanent (open-ended) contract.
Table 2a. Effect of contract type on log wages.
OLS Fixed Effects
Open-ended contract 0.123 ** 0.117 ***
(0.012) (0.012)
Observations 9.702 9.702
NOTE: ** 5% level of significance; *** 1% level of significance.
The dependent variable in all regressions is log monthly wages.
Regressions include a full range of controls: age, marital status, number of children, health, education, region, activity sector and year dummies. Robust standard errors are presented in parentheses.
Table 2b. Effect of marital status on log wages.
Overall Model
(FE)
Open-Ended
(FE)
Temporary
(FE)
Married 0.051 *** 0.067 *** 0.097***
(0.015) (0.018) (0.028)
Observations 9.702 6.584 3.118
NOTE: *** 1% level of significance.
The dependent variable in all models is log monthly wages.
The models all show the estimates attached to the “Married” variable. All models include a full range of controls: age, number of children, health, education, region, activity sector and year dummies. Robust standard errors are presented in parentheses.
Table 3. Effect of marital status on log wages by level of education.
Degree or more Higher school Lower school or less
Open-
Ended (FE)
Temporary
(FE)
Open-
Ended (FE)
Temporary
(FE)
Open-
Ended (FE)
Temporary
(FE)
Married 0.075 *** 0.141 *** 0.209 *** -0.038 -0.027 0.034
(0.031) (0.067) (0.038) (0.068) (0.026) (0.034)
Observations 2.145 612 1.430 599 3.009 1.907
NOTE: *** 1% level of significance.
The dependent variable in all models is log monthly wages.
The models all show the estimates attached to the “Married” variable. All models include a full range of controls: age, number of children, health, region, activity sector and year dummies. Robust standard errors are presented in parentheses.
Table 4. Effect of marital status on log wages by level of education.
Group A Group B
Open-Ended (FE) Temporary (FE) Open-Ended (FE) Temporary (FE)
Married 0.095 *** 0.140 *** -0.027 -0.039
(0.024) (0.067) (0.025) (0.030)
Observations 3.575 612 3.009 2.506
NOTE: ***: 1% level of significance.
The dependent variable in all models is log monthly wages.
The models all show the estimates attached to the “Married” variable. All models include a full range of controls: age, number of children, health, region, activity sector and year dummies. Robust standard errors are presented in parentheses.
Table A5a. The coefficient linked to “Permanent Contract” - only married men.
OLS Fixed Effects
Permanent Contract -0,016 ** -0,015 *
(0,009) (0,009)
Observations 6.462 6.462
NOTE: ***: y 1% level of significance.
The dependent variable in all models is log monthly wages.
The models all show the estimates attached to the “Permanent Contract” variable. All models include a full range of controls: age, marital status, number of children, health, education, region, activity sector and year dummies. Clustered standard errors are presented in parentheses.
Table A5b. The coefficient linked to “Permanent contract” – never married men.
OLS Fixed Effects
Permanent Contract 0,081 *** 0,064 ***
(0,012) (0,011)
Observations 14.867 14.867
NOTE: ***: y 1% level of significance.
The dependent variable in all models is log monthly wages.
The models all show the estimates attached to the “Permanent Contract” variable. All models include a full range of controls: age, marital status, number of children, health, education, region, activity sector and year dummies. Clustered standard errors are presented in parentheses.